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On the Steiner System Ssystem $S(4,5,11)$

Is there a nice way to partition the edges of the complete 5$5$-uniform hypergraph on 11$11$ vertices into 7$7$ copies of the Steiner system S(4,5,11)$S(4,5,11)$? If this is obvious or elementary, I apologize in advance.

On the Steiner System S(4,5,11)

Is there a nice way to partition the edges of the complete 5-uniform hypergraph on 11 vertices into 7 copies of the Steiner system S(4,5,11)? If this is obvious or elementary, I apologize in advance.

On the Steiner system $S(4,5,11)$

Is there a nice way to partition the edges of the complete $5$-uniform hypergraph on $11$ vertices into $7$ copies of the Steiner system $S(4,5,11)$? If this is obvious or elementary, I apologize in advance.

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user48028
user48028

On the Steiner System S(4,5,11)

Is there a nice way to partition the edges of the complete 5-uniform hypergraph on 11 vertices into 7 copies of the Steiner system S(4,5,11)? If this is obvious or elementary, I apologize in advance.